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21st Cumberland Conference on Graph Theory, Combinatorics, and Computing ---In Honor of Mike Plummer's 70th Birthday
May 15-17, 2008
Vanderbilt University
Nashville, TN, USA

Organizers
Mark Ellingham and Gexin Yu

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Graceful number and Harmonious Number of a Graph
by
G. Sethuraman
Universiti Teknologi Petronas, Bandar Seri Iskandar, 31750 Tronoh, Perak Darul Ridzuan, Malayasia
Coauthors: K. Sankar

Sethuraman and Elumalai [G. Sethuraman, A. Elumalai, Packing any sets of graphs into a graceful /harmonious/elegant graph, Ars Comb.76 (2005)] have proved a structurally important result that for every graph G there exists a graceful (harmonious) graph containing G as its vertex induced subgraph. It is more interesting and significant to understand the existence of the smallest graceful(harmonious) graph containing the given graph as its vertex induced subgraph. Motivated by this, here we introduce two new graph parameters, graceful number and harmonious number of a graph and we determine the graceful number of the well known nongraceful graphs, K5 , K6 , C4k+1, and C4k+2 and the harmonious number of C4 and K5.

Date received: February 22, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawn-03.